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Pseudo-normal form near saddle-center or saddle-focus equilibria
Delshams Valdés, Amadeu; Lázaro Ochoa, José Tomás
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
In this paper we introduce the pseudo-normal form, which generalizes the notion of normal form around an equilibrium. Its convergence is proved for a general analytic system in a neighborhood of a saddle-center or a saddle-focus equilibrium point. If the system is Hamiltonian or reversible, this pseudo-normal form coincides with the Birkhoff normal form, so we present a new proof in these celebrated cases. From the convergence of the pseudo-normal form for a general analytic system several dynamical consequences are derived, like the existence of local invariant objects.
Differential equations
Global analysis (Mathematics)
Normal Forms
Pseudo-normal forms
Hamiltonian and reversible systems
Equacions diferencials ordinàries
Varietats (Matemàtica)
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::58 Global analysis, analysis on manifolds
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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